This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces approach defined by the Enneper-Weierstrass formula for immersion and the solutions of the Gauss-Weingarten equations for moving frames, we derive the three-dimensional numerical representation for these polynomials. We illustrate the theoretical results for several examples, including the Bessel, Legendre, Laguerre, Chebyshev and Jacobi functions. In each case, we generate a numerical representation of the surface using the Mathematica symbolic software.

中文翻译：

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与正交多项式相关的最小曲面

本文致力于研究欧几里得或双曲空间中二维曲面的浸没函数与经典正交多项式之间的联系。在简要描述由 Enneper-Weierstrass 浸没公式定义的孤子面方法和运动坐标系的 Gauss-Weingarten 方程的解之后，我们推导出这些多项式的三维数值表示。我们说明了几个例子的理论结果，包括贝塞尔函数、勒让德函数、拉盖尔函数、切比雪夫函数和雅可比函数。在每种情况下，我们都使用 Mathematica 符号软件生成表面的数字表示。